我们展示了如何利用持续性（persistence）来度量有限单纯复形中上同调圈的鲁棒性。我们引入两类不变量：厚贝蒂数（thick Betti numbers），用于度量连通分支与洞是否由足够高维的单纯形所支撑；凝聚贝蒂数（cohesive Betti numbers），用于度量支撑上同调类的高阶邻接关系的强度。随后，我们通过将攻击参数与厚参数或凝聚参数相结合，并借助其像、核与余核持续性模（image, kernel, and cokernel persistence modules）分析所得阶梯模（ladder modules），研究单纯复形退化过程下的鲁棒性。这使我们能够区分在退化过程中保持结构鲁棒性的特征与失去厚度或凝聚性的特征。最后，我们利用第二网络距离（second network distance）证明了稳定性结果，从而为所提出的构造提供了理论可靠性保证。

We show how persistence can be used to measure the robustness of cohomological cycles in finite simplicial complexes. We introduce two families of invariants: thick Betti numbers, which measure whether connected components and holes are supported by simplices of sufficiently high dimension; and cohesive Betti numbers, which measure the strength of higher-order adjacencies supporting cohomology classes. We then study robustness under simplicial degradation processes by combining an attack parameter with either the thick or the cohesive parameter, and by analyzing the resulting ladder modules through their image, kernel, and cokernel persistence modules. This allows us to distinguish features that remain structurally robust from those that lose thickness or cohesion during the degradation process. Finally, we prove stability results using the second network distance, which provides a theoretical reliability guarantee for the proposed constructions.